in my opinion a sterilite with holes in it is just not enough ventillation for mice. you could cut a section out of the top and use mesh wire to cover it--this will provide much more ventillation. either way the mice will chew any holes you put in the lid if they can reach them and will chew their way out of the tub so i'd advise something tall enough that they can't get to the lid.

i have 2 female mice that are basically just pets and i keep them in a wire cage for maximum ventillation/non-chewage. i also use a product called stall dry from my local feed store--this cuts down on the ammonia smell by far. i use it in all my rats bins as well. before i started using it the mice were ridiculously stinky but it really does help with that.